For some reason, regardless of looks, I often end up liking the comic-relief sort of guy.

Literal

I [topic-は] somehow, looks [regardless of-に関わらず] third-character [genitive-の] person [object-を] become-to-like [thing-が] many is [explanatory-なん] is.

A self-analysis of romantic preferences. 三枚目 (さんまいめ) is a fascinating word borrowed from kabuki theater: originally the third name on a kabuki bill, which was reserved for the comic actor. It's come to mean 'the comic-relief type,' 'the funny one,' 'the goofball' — someone who's funny and approachable rather than handsome. Contrasts with 二枚目 ('second on the bill' = the handsome leading man) and 一枚目 (the top-billed star). This theatrical metaphor is still alive in everyday speech for describing personality types. ~に関わらず ('regardless of X') is a formal phrase for 'regardless of.'